Nonexplicit Singular Perturbations and Interconnected Systems

Singular perturbations have been shown to be an effective tool in the analysis and design of systems with "slow" and "fast" dynamics. However, the use of this tool is often inhibited by the fact that when physical quantities are selected as state variables the model fails to be in the standard singularly perturbed form. In this thesis we deal with such nonexplicit models and show that for a wide class of problems a proper selection of variables leads to explicit singularly perturbed models. Equilibrium and conservation properties are shown to provide a coordinate-free characterization of two-time-scale systems. They also suggest a coordinate transformation that transforms nonexplicit models into explicit ones. This transformation is then used to study nonlinear high gain feedback systems, thus extending earlier linear results. It is also utilized to establish the relation between weak connections and time scales in interconnected systems whose subsystems possess a continuum of equilibrium points. Finally, the methodology is applied to reduced order modeling of dynamic networks and it is shown that linear conservation laws lead to a linear transformation separating the time scales even when some of the components of the network are nonlinear. Moreover, the reduced order model retains the physical meaning of the original system.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Peponides, George Michael

• Engineering, Electronics and Electrical

Identifier

(UMI)AAI8302959

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/69241